13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- to the conclusion that foil thickness materials should have smaller z values, however compared to the dependence on yield strength and fracture toughness, z has a weaker, square-root, dependence on h. Although the mode I fracture toughness KIc and yield strength �y of 30 �m pure Ti foil were not determined in the present investigation, it can be expected, in line with results for foil-thickness metals, that the mode I fracture toughness KIc decreases with decreasing sample thickness [10]. Therefore it is indicated from the slightly higher value of m that although the sample thickness h decreases for foils, the effect of �y/KIc on the similarity parameter of z is more significant. The foil samples investigated also demonstrated complicate ductile combined brittle fatigue fractures features (Fig. 7). The fatigue behavior of the Ti foils, which was characterized by slightly elevated m values and both ductile and brittle fracture surface characteristics, is consistent with the speculation that the higher m value induced by higher z value with decreasing sample characteristic dimension h, fracture toughness Kc and increasing yield strength �y. To summarize, a preliminary incomplete self-similarity analysis, indicates that that the slightly higher m values observed for the Ti foil specimens, and in other metal foils [5, 6] is related to a the reduction in the fracture toughness and the rising in the yield strength with decreasing metal thickness. It can also be inferred from the incomplete similarity that with a further decrease in fracture toughness with decreasing thickness even higher values of m indicative brittle crack growth could occur. 6. Conclusions A new experimental approach to study the tensile fatigue behavior of ultra-thin metal foils was developed. The technique, which involves magnetic coupling between an eccentric steel rotor and a ceramic magnet attached to a specimen grip mounted to a linear bearing slide. Cyclic tensile loads are induced in the specimen during rotation of the eccentric disk which is attached to a variable speed DC motor. The apparatus can be readily fit with a small furnace for testing at elevated temperatures. For the proof-of-concept experiments, fatigue crack growth tests were performed with commercially pure 0.03 mm thick Ti foils. Based on the observations, test results and a preliminary similarity analysis, the following conclusions can be made: 1. The test apparatus shows considerable promise as a low-cost method to study tensile fatigue and mode I cyclic crack growth of thin foils and wires at ambient and elevated temperatures. 2. Analysis showed that a shift in the centerline of loading can occur when testing edge-notched specimens, which induces an opening moment at the crack tip. If not accounted for, this effect can lead to overestimation of the mode I stress intensity factor. 3. Crack growth data for specimens with the same notch-to-width ratios, exhibits similar trends and fatigue crack growth parameter values. For all test cases, stable crack growth was observed. 4. The effective stress intensity factor �KI corrected by FEM analysis for face-loaded specimens were used to correlate the crack growth rate da/dN. The crack growth rate can be described by a Paris relationship with a m value between 4~5. The results are consistent with other studies of thin metal foils where high m values are commonly observed. An incomplete self-similarity theory was used to gain additional insight to the higher m value in Paris law and possible trends with decreasing specimen thickness. It is proposed that due to a significant reduction in fracture toughness KIc for foil thickness metals, the basic similarity parameter z increases, which leads to an increasing m value. This also infers that there is a transition
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